Sylvia likes to walk to work when the weather is nice. She works at the bank at the corner of 41st Street and Edison Avenue. Her house is at the corner of 42nd Street and Johnson Avenue. She can walk down Johnson Avenue and turn right on 41st Street, or she can walk through the park. The distance from 42nd Street to 41st Street is 80 yards, and it is 60 yards from Johnson Avenue to Edison Avenue. Assuming the street intersections are 90° angles, how much shorter is it for Sylvia to walk through the park? (1 point) If Sylvia walks through the park instead of straight down Johnson Avenue and straight down 41st Street, the walk will be

Answer 1

To determine how much shorter it is for Sylvia to walk through the park compared to walking down Johnson Avenue and turning on 41st Street, we need to calculate the distances for both routes.

1. Walking Down Johnson Avenue and Turning on 41st Street:

   • The distance from 42nd Street to 41st Street is 80 yards (this is the distance she will walk down Johnson Avenue).
   • The distance from Johnson Avenue to Edison Avenue is 60 yards (this is the distance she will walk on 41st Street).
   • Total distance = 80 yards + 60 yards = 140 yards.

2. Walking Through the Park:

   • When walking through the park, Sylvia effectively walks diagonally, forming a right triangle with:
     • The horizontal leg being the 80 yards from 42nd Street to 41st Street.
     • The vertical leg being the 60 yards from Johnson Avenue to Edison Avenue.
   • We can use the Pythagorean theorem to find the diagonal distance (d): \[ d = \sqrt{(80^2 + 60^2)} = \sqrt{(6400 + 3600)} = \sqrt{10000} = 100 \text{ yards} \]

3. Calculating the Difference:

   • The distance walking through the park is 100 yards.
   • The distance walking down Johnson Avenue and then turning on 41st Street was 140 yards.
   • The difference is: \[ 140 - 100 = 40 \text{ yards} \]

Therefore, walking through the park is 40 yards shorter than walking down Johnson Avenue and then turning on 41st Street.